Question: Solve for $x$ and $y$ using substitution. ${6x+4y = 4}$ ${y = -3x-5}$
Solution: Since $y$ has already been solved for, substitute $-3x-5$ for $y$ in the first equation. ${6x + 4}{(-3x-5)}{= 4}$ Simplify and solve for $x$ $6x-12x - 20 = 4$ $-6x-20 = 4$ $-6x-20{+20} = 4{+20}$ $-6x = 24$ $\dfrac{-6x}{{-6}} = \dfrac{24}{{-6}}$ ${x = -4}$ Now that you know ${x = -4}$ , plug it back into $\thinspace {y = -3x-5}\thinspace$ to find $y$ ${y = -3}{(-4)}{ - 5}$ $y = 12 - 5$ $y = 7$ You can also plug ${x = -4}$ into $\thinspace {6x+4y = 4}\thinspace$ and get the same answer for $y$ : ${6}{(-4)}{ + 4y = 4}$ ${y = 7}$